can anyone tell me how many combinations of numbers from 1 to 5 are, for example, 1-2-3-4-5, 2-1-3-4-5, 2-3-1-4-5, and so on.
and what are those combinations.

Thanks

ps:I'm sorry if this is not the right place to post this question

May 13th 2009, 01:37 PM

Plato

May 13th 2009, 01:41 PM

jcamilo

thanks for your quick reply, i also wanted to know what are those combinations, is there an easy way to know?

May 13th 2009, 01:43 PM

Plato

Quote:

Originally Posted by jcamilo

I so wanted to know what are those combinations, is there an easy way to know?

The list is 120 long.
No there is no easy way to do it.

May 13th 2009, 01:58 PM

jcamilo

Ok thanks a lot

May 13th 2009, 06:07 PM

Media_Man

Permutations

Technically, what you are asking for are the permutations of . Consider - you have five blank slots in which to fill five distinct objects:

1 2 3 4 5

_ _ _ _ _

For the first blank, you have five options to choose from, for example,

1 2 X 4 5

3 _ _ _ _

For the next blank, you have four options, etc, all the way down to the last blank, in which you only have one option, whatever number is left over. By the Fundamental Counting Principal, you get your total number of options by multiplying all these individual options together, thus getting , as Plato has shown.

There is a simple and organized way of writing all of these down, and I'll use the 4 case to show you, since indeed 5 is too long. 4!=24, so there are 24 permutations in the set. A fourth of them start with one, a fourth start with 2, etc. In the fourth starting with one, a third have a next number of 2, a third have a next number of 3, etc. Repeat this process and you will see an easy pattern emerge: